How do you solve: x^6+26x^3-27=0?

jason01

How do you solve: x^6+26x^3-27=0?
I have tried few method, but Im not 100% sure.

Reply 1

synaesthesia

jason01

How do you solve: x^6+26x^3-27=0?
I have tried few method, but Im not 100% sure.

Factorise to give

(X^3 +27)(X^3-1)=0

It should be straightforward from there.

Reply 2

Dekota

jason01

How do you solve: x^6+26x^3-27=0?
I have tried few method, but Im not 100% sure.

synaesthesia

Factorise to give

(X^3 +27)(X^3-1)=0

It should be straightforward from there.

So:
x^6+26x³-27 = 0
=> (x³ + 27)(x³ - 1) = 0

=> (x³ - 1) = 0
=> x³ = 1
=> x = 1

=> (x³ + 27) = 0
=> x³ = -27
=> x = -3

Reply 3

Charli88

Hey, i'm not good at maths so i apologise if this if wrong, but i think its a disguised quadratic, so if you make x^3=y then the equation looks like:
y^2 + 26y -27 = 0
(y+27)(y-1)
y=-27 or y= 1
so therefore,
x^3= -27 or x^3=1

then just cube root them, i reckon

Am i anywhere near right?
Hope this helps xxx

Reply 4

sugarwhirl89

Both methods give the same answer - it just depends which you're most comfortable with :P

Reply 5

jason01

Thanks guys
The working out on the mark-scheme is completely different, so I’ve been trying to figure out how the examinees got the answer using your solutions for this problem.